incompetence vs unfitness

incompetence and unfitness both are nouns.

Word	Noun	Adjective	Verb	Adverb
incompetence	Yes	No	No	No
unfitness	Yes	No	No	No

As nouns, unfitness is a hypernym of incompetence; that is, unfitness is a word with a broader meaning than incompetence:

Other hypernyms of incompetence include inability.

incompetence (noun)	unfitness (noun)
lack of physical or intellectual ability or qualifications	the quality of not being suitable
inability of a part or organ to function properly	lacking the power to perform
	poor physical condition; being out of shape or out of condition (as from a life of ease and luxury)